A342922 Numbers k such that A342925(k) = k + 2*A003415(k).

6, 28, 29, 496, 857, 1721, 8128, 164284, 6511664, 33550336, 400902412, 8589869056

Offset: 1

Author

Antti Karttunen, Apr 07 2021

Keywords

• nonn
• more

Comments

Question: Are all odd terms in A001359?

Certainly any prime p such that A003415(p+1) = p + 2 satisfies the equation. See comments in A007850.

Links

• Index entries for sequences where odd perfect numbers must occur, if they exist at all

Crossrefs

Cf. A000396 (subsequence), A001359, A003415, A007850.

Cf. A203617, A342923, A342924, A342925.

Programs

Mathematica

Select[Range[2*10^5], #3 == #1 + 2 #2 & @@ Prepend[Map[If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &, {#, DivisorSigma[1, #]}], #] &] (* Michael De Vlieger, Feb 25 2022 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A342925(n) = A003415(sigma(n));
isA342922(n) = (A342925(n)==(n+(2*A003415(n))));

Extensions

Terms a(11) and a(12) from Antti Karttunen, Feb 25 2022